Bound values for Hall conductivity and percolation under quantum Hall effect conditions

The percolation under Quantum Hall Effect conditions in inhomogeneous medium has been studied. The lower and upper bound possible values for effective Hall conductivity values have been established. It has been shown that these bound values for Hall conductivity differ from bound values for metal conductivity. It comes from unusual character of current percolation under Quantum Hall Effect conditions. The physical sense of obtained results has been discussed.